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This paper presents the applications of the level set function for identification the unknown shape of an interface motivated by Electrical Impedance Tomography (EIT). A new approach was adopted based on a continuous approximation of material coefficient distribution using level set methods and the finite element method. A model problem in electrical impedance tomography for the identification of unknown shapes from data in a narrow strip along the boundary of the domain is investigated.
Rocznik
Tom
Strony
105--108
Opis fizyczny
Bibliogr. 15 poz.
Twórcy
Bibliografia
- BOLKOWSKI S., STABROWSKI M, SKOCZYLAS J., SROKA J., SIKORA J., WINCENCIAK S., (1993), Komputerowe metody analizy pola elektromagnetycznego. WNT, Warszawa.
- CHOPP D.L., (2000), The Level-Set Method for Simulating Island Coarsening, Journal of Computer Physics, Vol. 162, pp. 104-122.
- DENG S., ITO K., LI Z., (2003), Three dimensional elliptic solvers for interface problems and applications, Journal of Computer Physics, Vol. 184, pp. 215-243, 2003.
- FILIPOWICZ S.F., RYMARCZYK T., (2003), Tomografia Impedancyjna, pomiary, konstrukcje i metody tworzenia obrazu. BelStudio, Warsaw.
- FILIPOWICZ S.F., RYMARCZYK T., SIKORA J., (2004), Level Set Method for Inverse Problem Solution In Electrical Impedance Tomography. Proceedings of the XII International Conference on Electrical Bioimpedance & V Electrical Impedance Tomography, p.519-522, Gdansk.
- GAO H., LI Z., ZHAO H., (1999), A Numerical Study of Electro-migration Voiding by Evolving Level Set Functions on a Fixed Cartesian Grid, Journal of Computer Physics, Vol. 152, pp. 281-304.
- HOU T., LI Z., OSHER S., ZHAO H., (1997), A hybrid method for moving interface problems with application to the Hele-shaw flow, Journal of Computer Physics, Vol. 134, pp. 236-252.
- ITO K., KUNISH K., LI Z., (2001), The Level-Set Function Approach to an Inverse Interface Problem, Inverse Problems, Vol. 17, pp. 1225-1242.
- LI Z., (1998), A fast iterative algorithm for elliptic interface problems, SIAM Journal of Numerical Analysis, Vol. 35, pp. 230-254.
- OSHER S., FEDKIW R., (2003), Level Set Methods and Dynamic Implicit Surfaces. Springer, New York.
- OSHER S., SETHIAN J.A., (1988), Fronts Propagating with Curvature Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations, Journal of Computer Physics, Vol. 79, pp. 12-49.
- RYMARCZYK T., FILIPOWICZ S.F., SIKORA J., (2008), Level Set Method in Electrical Impedance Tomography, 2nd Symposium on Applied Electromagnetics SAEM'08, Zamosc.
- SETHIAN J.A., (2008), Level Set Methods and Fast Marching Methods. Cambridge Univeristy Press.
- SIKORA J., (2000), Algorytmy numeryczne w tomografii impedancyjnej i wiroprądowej. WPW, Warszawa.
- ZHAO, H.-K., OSHER, S. and FEDKIW, R., (2001), Fast Surface Reconstruction using the Level Set Method. 1st IEEE Workshop on Variational and Level Set Methods, in conjunction with the 8th International Conference on Computer Vision (ICCV), Vancouver, Canada, pp. 194-202.
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Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD1-0020-0032